Quantum morphogenesis: A variation on Thom's catastrophe theory

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 5 1, 2003, Pages

  Aerts, Diederik ^a   Czachor, Marek ^b   Gabora, Liane ^a   Kuna, Maciej ^b   Posiewnik, Andrzej ^c   Pykacz, Jaroslaw ^c   Syty, Monika ^b  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b GDANSK UNIVERSITY OF TECHNOLOGY   (Poland)

^c UNIVERSITY OF GDA SK   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

HAMILTONIANS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; PROBABILITY; RANDOM PROCESSES; STATISTICAL METHODS; VECTORS;

HILBERT SPACE MODEL; QUANTUM MORPHOGENESIS; THOM CATASTROPHE THEORY; VON NEUMANN EQUATION;

QUANTUM THEORY;

EID: 42749098019     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. R. Thom, Structural Stability and Morphogenesis: An Outline of a General Theory of Models (Benjamin, Reading, MA, 1975).
2. E.G. Beltrametti and G. Cassinelli, The Logic of Quantum Mechanics (Addison-Wesley, Reading, MA, 1981).
3. D. Aerts and S. Aerts, Found. Sc. 1, 85 (1994).
4. L. Gabora, Doctoral thesis, CLEA, Brussels Free University, 2001.
5. D. Aerts, B. Coecke, and B. D'Hooghe, Helv. Phys. Acta 70, 793 (1997).
6. D. Aerts, S. Aerts, J. Broekaert, and L. Gabora, Found. Phys. 30, 1387 (2000).
7. E.W. Piotrowski and J. Sladkowski, Acta Phys. Pol. B 32, 3873 (2001).
8. D. Aerts, J. Math. Phys. 24, 2441 (1983).
9. V.P. Belavkin and V.P. Maslov, Theor. Math. Phys. 33, 17 (1977).
10. S. Gheorghiu-Svirschevski, Phys. Rev. A 63, 022105 (2001).
11. J. Sladkowski, e-print cond-mat/0211083.
12. L. Glass and M.C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988).
13. J.D. Murray, Nonlinear Differential Equation Models in Biology (Clarendon, Oxford, 1977).
14. P.C. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics Vol. 28 (Springer, New York, 1979).
15. J. Swift and P.C. Hohenberg, Phys. Rev. A 15, 319 (1977).
16. L.N. Howard and N. Kopell, Stud. Appl. Math. 56, 95 (1977).
17. V.L. Ginzburg and L.D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950).
18. K. Stewartson and J.T. Stuart, J. Fluid Mech. 48, 529 (1971).
19. A. Gierer and H. Meinhardt, Kybernetik 12, 30 (1972).
20. W. Kemmer, Differentiation 26, 83 (1984).
21. M. Czachor, Phys. Lett. A 225, 1 (1997).
22. M. Czachor and J. Naudts, Phys. Rev. E 59, R2497 (1999).
23. S.B. Leble and M. Czachor, Phys. Rev. E 58, 7091 (1998).
24. M. Czachor, H. D. Doebner, M. Syty, and K. Wasylka, Phys. Rev. E 61, 3325 (2000).
25. N.V. Ustinov, M. Czachor, M. Kuna, and S.B. Leble, Phys. Lett. A 279, 333 (2001).
26. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
27. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
28. D.M. Greenberger, M.A. home, A. Shimony, and A. Zeillinger, Am. J. Phys. 58, 1131 (1990).
29. D. Aerts, J. Math. Phys. 27, 202 (1986).
30. S. Bergia, F. Cannata, A. Cornia, and R. Livi, Found. Phys. 10, 723 (1980).
31. N.D. Mermin, Am. J. Phys. 66, 753 (1998).
32. C. Walter, R. Parker, and M. Ycas, J. Theor. Biol. 15, 208 (1967).
33. L. Glass and S.A. Kauffmann, J. Theor. Biol. 34, 219 (1972).
34. L. Glass and S.A. Kauffman, J. Theor. Biol. 39, 103 (1973).
35. J.J. Hopfield and D.W. Tank, Science (Washington, DC, U.S.) 233, 625 (1986).
36. C. Tsallis, R.S. Mendes, and A.R. Plastino, Physica A 261, 534 (1998).
37. S.A. Kauffman, The Origins of Order. Self-Organization and Selection in Evolution (Oxford University Press, Oxford, 1993).
38. E.C. Zeeman, Int. J. Neurosci. 6, 39 (1973).
39. R. Thom, in Towards a Theoretical Biology, edited by C.H. Waddington (Aldine, Chicago, 1970), Vol. 3.